To assess the accuracy of the boy's claim that the area of the lawn is 300 square feet, we need to determine the areas of both the path and the yard, and then see how the path influences the total area of the lawn.
1. Calculate the Area of the Path:
- The length of the path is 40 feet.
- The width of the path is 4 feet.
- Therefore, the area of the path is given by:
[tex]\[
\text{Area of the path} = \text{Length} \times \text{Width} = 40 \text{ ft} \times 4 \text{ ft} = 160 \text{ sq ft}
\][/tex]
2. Evaluate the Boy’s Claim (Understanding the Yard and Lawn Area):
- The boy claims the lawn's area is 300 square feet, which he describes as half the yard’s area.
- One-half of the yard area indeed means that the complete yard area the boy is assuming must be:
[tex]\[
\text{Full yard area} = 2 \times \text{Lawn area claimed by boy} = 2 \times 300 \text{ sq ft} = 600 \text{ sq ft}
\][/tex]
3. Validate the Correct Area of the Lawn:
- The yard's total area is confirmed as 600 square feet.
- With the path occupying 160 square feet, the remaining area, which will be the lawn's area, can be calculated by subtracting the path's area from the total yard:
[tex]\[
\text{Lawn area} = \text{Total yard area} - \text{Area of the path} = 600 \text{ sq ft} - 160 \text{ sq ft} = 440 \text{ sq ft}
\][/tex]
Based on the above steps, we see that the lawn would indeed have an area of 440 square feet, not 300 square feet. Therefore, the boy's claim is incorrect.
The correct statement is:
- He is incorrect. The path will have an area of [tex]\( (4)(40) = 160 \, \text{sq ft} \)[/tex]. The yard has an area of [tex]\( 600 \, \text{sq ft} \)[/tex]. The area of the lawn will be the difference between the yard and path, so it is [tex]\( 440 \, \text{sq ft} \)[/tex].
